Question
A cricket team of 9 players is to be formed from 10
batsmen and 6 bowlers. Find the number of ways to form the team such that at least 7 batsmen are selected.Solution
Case I: 7 batsmen and 2 bowlers:
10C7 × 6C2 = 120 × 15 = 1800
Case II: 8 batsmen and 1 bowler:
10C8 × 6C1 = 45 × 6 = 270
Case III: 9 batsmen and 0 bowlers:
10C9 × 6C0 = 10 × 1 = 10
Total = 1800 + 270 + 10 = 2080 ways
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